Abstract

The trace of a function, its restriction to the boundary of the definition domain, is a fundamental concept in the study of boundary value problems for partial differential equations (PDEs). While trace operators on Sobolev spaces are well understood in the context of elliptic PDEs, such spaces are ill-suited for advection operators due to their directional derivatives. In this talk, we make a remark on the boundedness of the trace operator on a function space tailored to advection operators, and present how to investigate boundary value problems on such spaces with the trace operator. This argument also works for kinetic equations including the stationary Boltzmann equation. This talk is partially based on a joint work with Dr. Masaki  Imagawa (Academia Sinica).

 

Organizer: I-Kun Chen ( NTU)